ENGR 1310 Introduction to Mechanical Engineering Fundamentals Spring 2013 Dr. Paul Griesemer

Case Study in Mechanical Engineering: Bridge Construction Why do bridges look the way they do? – Many different shapes, sizes, construction techniques

What are the design issues in bridge construction? What are we trying to optimize with the “best” design – Strength – Safety – Cost Materials Complexity Longevity Suspension – Low cost over large spans Arch – Strong, durable Truss – Simple, small members over small spans

Types of Bridges Pier & Beam (or just Beam) –BP Pedestrian Bridge in Millennium Park, Chicago, Illinois

Types of Bridges Suspension (or Cable-stayed) –Akashi-Kaikyō Bridge (or Pearl Bridge) over the Akashi Strait in Japan –World's longest spanning suspension bridge

Types of Bridges Arch Bridge –Si-o-se Pol bridge over Zayandeh River in Esfahan, Iran

Types of Bridges Truss Bridge –Kingston-Rhinecliff Bridge over Hudson River, New York, USA

Our goal will be to understand the basic design and analysis methods Our “design project” will be a truss structure – Predict the strength properties

Engineering Analysis of a Truss What is the maximum load a structure can support? How do you design a structure to meet load requirements? How do you determine the forces in each member of the truss? Answer: Mechanics

Mechanics Statics – Nothing accelerating – Not time dependent Dynamics – Forces lead to acceleration – Translation and rotation

Background: Forces and Vectors In both Statics and Dynamics, forces must be treated as vectors. Scalars – Have only a magnitude – Examples: Volume Time Mass Vectors – Have magnitude and direction – Examples Velocity Position Acceleration

Addition of Vectors Vectors are added “tip to tail” – Vectors don’t have a designated location F2F2 F1F1 F 1 + F 2

Components of a Vector Similarly, vectors can be broken into smaller vectors whose addition equals the original F FxFx FyFy

Picture Frame Example: What is the best way to hang a 40 lb mirror on a wall? How much tension is in the hanger wire in each case? Option 1: One Hanger in Wall Option 2: Two Hangers in Wall 48 in 12 in